Optimal placement method and system of traveling wave positioning device for multi-branch complex distribution network

Abstract

This application discloses an optimized deployment method and system for traveling wave location devices in complex multi-branch distribution networks. It transforms the topology of a radial distribution network into a tree-like hierarchical model, establishes a linear constraint system for observable faults across the entire network based on the adjacency relationship between parent and child nodes, and then constructs a zero-one-integer programming model with the objective of minimizing the total number of devices installed. A weighted adjustment of the objective function is made by introducing a combined weight of line length and historical fault frequency. Finally, an accurate solution is achieved through a mixed-integer linear programming solver. This approach significantly reduces the number of traveling wave location devices required, substantially lowers equipment investment costs, and ensures that the optimization results are globally optimal and reproducible. Furthermore, the weighted mechanism ensures that the deployment scheme is highly adaptable to the actual operating conditions of the distribution network, effectively enhancing the engineering practical value of fault location.

Description

Technical Field

[0001] This application relates to the field of optimized placement, and more specifically, to a method and system for optimized placement of traveling wave positioning devices in complex multi-branch distribution networks. Background Technology

[0002] With the continuous expansion of distribution network scale and the large-scale integration of distributed power sources, modern distribution networks exhibit significant characteristics such as numerous branch lines, complex topologies, and flexible and varied operating modes. Rapid and accurate fault location has become a crucial link in ensuring power supply reliability and improving operation and maintenance efficiency. Traveling wave (TW) positioning technology, with its inherent advantages such as high ranging accuracy and immunity to transition resistance and system oscillations, is gradually being promoted and applied from transmission networks to distribution networks. However, distribution networks generally adopt a radial tree-like power supply structure with a large number of branch nodes. Deploying TW devices at the ends of all lines would lead to a sharp increase in equipment investment costs, making it economically unacceptable. Conversely, if the number of devices is insufficient or their placement is unreasonable, it cannot be guaranteed that faults occurring at any location in the entire network can be effectively detected and located, creating observation blind spots. Therefore, how to achieve optimal placement with the fewest devices while ensuring network-wide fault observability is a core problem that urgently needs to be solved in the engineering application of TW technology in distribution networks.

[0003] Existing methods for deploying traveling wave (TW) location devices suffer from the following technical shortcomings. One type of method follows the dual-end ranging approach of transmission networks, requiring the installation of TW acquisition devices at all endpoints of the distribution network. While this simplifies the processing logic of intermediate nodes, the number of endpoints remains considerable in complex distribution networks with numerous branches, and the total number of devices is not substantially optimized. Another type of method uses graph theory's minimum dominator set theory combined with intelligent optimization algorithms such as genetic algorithms to solve for the deployment scheme. Although this can reduce the number of devices to some extent, it only guarantees that the fault signal is detected by a single device, failing to strictly distinguish between directly observable and indirectly observable faults. Furthermore, the heuristic algorithm itself lacks mathematical optimality guarantees, and the solution depends on the selection of the initial population and iteration parameters, resulting in poor reproducibility. In addition, the above methods generally fail to fully utilize the inherent tree-like topological hierarchy of the distribution network to construct accurate observability mathematical constraints, and do not incorporate factors reflecting actual engineering needs, such as differences in line length and the distribution of historical fault frequencies, into the optimization decision framework, leading to significant deficiencies in the engineering adaptability of the resulting deployment schemes.

[0004] Therefore, an optimized placement method for traveling wave positioning devices in complex multi-branch distribution networks is needed. Summary of the Invention

[0005] To address the aforementioned technical problems, this application provides a method and system for optimizing the placement of traveling wave positioning devices in complex multi-branch distribution networks.

[0006] According to one aspect of this application, a method for optimizing the placement of traveling wave location devices in a complex multi-branch distribution network is provided, comprising: S1. Based on the hierarchical topology of the radial distribution network, the obtained distribution network feature parameter set is recursively transformed into a tree structure to obtain the distribution network tree structure diagram. S2, based on the hierarchical adjacency relationship between parent and child nodes, performs fault observability constraint modeling on each local node set in the distribution network tree structure diagram to obtain a fault observability linear constraint set; S3, with the optimization objective of minimizing the total number of installed devices, assigns zero-one decision variables to all candidate nodes in the distribution network tree structure diagram, and embeds the fault observable linear constraint set as the solution boundary to obtain the point layout integer programming model; S4. Based on the line length data and historical fault frequency data, determine the comprehensive weight coefficient of each node, and perform weighted correction on the objective function of the integer programming model based on the comprehensive weight coefficient of each node to obtain the weighted integer programming model. S5 employs a mixed-integer linear programming solver to accurately solve the weighted point-based integer programming model, thereby outputting the optimal point-based scheme for whether or not to install traveling wave positioning devices at each candidate node.

[0007] According to another aspect of this application, an optimized deployment system for traveling wave location devices in a complex multi-branch distribution network is provided, comprising: The tree recursive transformation module is used to perform tree recursive transformation on the obtained distribution network feature parameter set based on the hierarchical topology of the radial distribution network to obtain the distribution network tree structure diagram. The fault observability constraint modeling module is used to perform fault observability constraint modeling on each local node set in the distribution network tree structure diagram based on the hierarchical adjacency relationship between parent and child nodes to obtain a fault observability linear constraint set. The minimization objective integer programming modeling module is used to minimize the total number of installed devices as the optimization objective. It assigns zero-one decision variables to all candidate nodes in the distribution network tree structure diagram and embeds the fault observable linear constraint set as the solution boundary to obtain the point layout integer programming model. The refined modeling module with comprehensive weight correction is used to determine the comprehensive weight coefficient of each node based on line length data and historical fault frequency data, and to perform weight correction on the objective function of the integer programming model based on the comprehensive weight coefficient of each node to obtain the weighted integer programming model. The mixed-integer programming exact solution module is used to use a mixed-integer linear programming solver to accurately solve a weighted point-based integer programming model and output the optimal point-based scheme for whether to install traveling wave positioning devices on each candidate node.

[0008] Compared with existing technologies, this application provides an optimized deployment method and system for traveling wave location devices in complex multi-branch distribution networks. It transforms the topology of the radial distribution network into a tree-like hierarchical model, establishes a linear constraint system for observable faults across the entire network based on the adjacency relationship between parent and child nodes, constructs a zero-one-integer programming model with the objective of minimizing the total number of devices installed, and introduces a weighted adjustment of the objective function using a combination of line length and historical fault frequency. Finally, an accurate solution is achieved through a mixed-integer linear programming solver. This approach significantly reduces the number of traveling wave location devices deployed, substantially lowers equipment investment costs, ensures global optimality and reproducibility of the optimization results, and the weighted mechanism ensures that the deployment scheme is highly adaptable to the actual operating conditions of the distribution network, effectively enhancing the engineering practical value of fault location. Attached Figure Description

[0009] The above and other objects, features, and advantages of this application will become more apparent from the more detailed description of the embodiments of this application in conjunction with the accompanying drawings. The drawings are provided to further illustrate the embodiments of this application and form part of the specification. They are used together with the embodiments of this application to explain this application and do not constitute a limitation thereof. In the drawings, the same reference numerals generally represent the same components or steps.

[0010] Figure 1 A flowchart illustrating the optimized placement method for traveling wave positioning devices in a multi-branch complex power distribution network according to an embodiment of this application; Figure 2 This is a data flow diagram illustrating the optimized placement method of traveling wave positioning devices in a multi-branch complex power distribution network according to an embodiment of this application. Figure 3 This is a flowchart of step S4 in the method for optimizing the placement of traveling wave positioning devices in a multi-branch complex power distribution network according to an embodiment of this application; Figure 4 A block diagram of an optimized deployment system for traveling wave positioning devices in a multi-branch complex power distribution network according to an embodiment of this application. Detailed Implementation

[0011] Hereinafter, exemplary embodiments according to this application will be described in detail with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of this application, and not all embodiments of this application. It should be understood that this application is not limited to the exemplary embodiments described herein.

[0012] As indicated in this application and claims, unless the context clearly indicates otherwise, the words "a," "an," "an," and / or "the" are not specifically singular and may include plural forms. Generally speaking, the terms "comprising" and "including" only indicate the inclusion of explicitly identified steps and elements, which do not constitute an exclusive list, and the method or apparatus may also include other steps or elements.

[0013] While this application makes various references to certain modules of the systems according to embodiments of this application, any number of different modules can be used and run on user terminals and / or servers. The modules described are merely illustrative, and different aspects of the systems and methods may use different modules.

[0014] Flowcharts are used in this application to illustrate the operations performed by the system according to embodiments of this application. It should be understood that the preceding or following operations are not necessarily performed in exact order. Instead, various steps can be processed in reverse order or simultaneously as needed. Furthermore, other operations can be added to these processes, or one or more steps can be removed from them.

[0015] In the technical solution of this application, an optimized placement method for traveling wave positioning devices in complex multi-branch distribution networks is proposed. Figure 1 This is a flowchart illustrating the optimized placement method for traveling wave positioning devices in a multi-branch complex power distribution network according to an embodiment of this application. Figure 2 This is a system architecture diagram of a method for optimizing the placement of traveling wave location devices in a multi-branch complex power distribution network according to an embodiment of this application. Figure 1 and Figure 2 As shown, the optimized placement method for traveling wave location devices in a multi-branch complex distribution network according to an embodiment of this application includes the following steps: S1, based on the hierarchical topology of the radial distribution network, a tree-shaped recursive transformation is performed on the obtained distribution network characteristic parameter set to obtain a distribution network tree structure diagram; S2, based on the hierarchical adjacency relationship between parent and child nodes, fault observability constraint modeling is performed on each local node set in the distribution network tree structure diagram to obtain a fault observability linear constraint group; S3, with the optimization objective of minimizing the total number of devices installed, zero-one decision variables are assigned to all candidate nodes in the distribution network tree structure diagram, and the fault observability linear constraint group is embedded as the solution boundary to obtain a placement integer programming model; S4, based on line length data and historical fault frequency data, the comprehensive weight coefficient of each node is determined, and the objective function of the placement integer programming model is weighted and corrected based on the comprehensive weight coefficient of each node to obtain a weighted placement integer programming model; S5, a mixed integer linear programming solver is used to accurately solve the weighted placement integer programming model to output the optimal placement scheme for whether to install traveling wave location devices at each candidate node.

[0016] Specifically, in S1, based on the hierarchical topology of the radial distribution network, the acquired set of distribution network characteristic parameters is recursively transformed into a tree-like structure to obtain a tree diagram of the distribution network. It should be understood that a radial distribution network adopts a single-source radial power supply structure, where electrical energy originates from the substation outlet and is transmitted layer by layer along the main line and branch lines to the end load nodes. This network topology inherently possesses a natural hierarchical recursive characteristic, meaning there is a unique power supply path from the root node on the power source side to each end load node, and there are clear upstream and downstream hierarchical relationships between nodes. However, the original distribution network topology data is usually stored in a flat form as a node-branch connection table, and the hierarchical membership and parent-child adjacency relationships between nodes are not explicitly expressed. To establish observable constraints for network-wide faults, in the technical solution of this application, firstly, the flat radial topology of the distribution network is transformed into a tree diagram with a clear hierarchical structure, so that the parent node, child node, and hierarchical depth of each node in the network are clearly identified. Specifically, the distribution network tree structure diagram is a rooted tree data structure obtained by transforming the radial distribution network topology. The root node is the first node of the main line, the last node of each branch line directly branching from the main line is a child node of the root node, the last node of each sub-branch branch is a child node of the next level, and so on, until all line end nodes are traversed. The construction of the tree structure diagram provides a structured topological foundation for subsequent fault observability constraint modeling, enabling constraints to be recursively generated layer by layer along the tree hierarchy, ensuring that all line segments in the entire network are included in the observability analysis scope.

[0017] The distribution network characteristic parameter set serves as the input data foundation for performing tree-like recursive transformation. It includes node sets, branch connection relationships, trunk line identifiers, line length data, and historical fault frequency data. The node set is a finite set of all electrical connection points in the distribution network; each node corresponds to a physical line segment endpoint, branch junction point, or end-load access point. Branch connection relationships describe whether there is a direct electrical connection line segment between any two nodes in the node set, and can be represented as an edge set or adjacency matrix of an undirected graph. Trunk line identifiers mark the main power supply channels from the substation outlet to the end of the line in the distribution network and are crucial for determining the root node of the tree structure.

[0018] In practice, firstly, based on the backbone line identifier, a head-end location search is performed in the node set to extract the power supply side endpoint with an in-degree of zero in the backbone line, and initialize it as the root node of the tree structure. Specifically, the backbone line identifier information is first read from the distribution network characteristic parameter set. This identifier clearly specifies the sequence of line segments in the distribution network that undertake the main power supply channel function. Then, in-degree statistical analysis is performed on all nodes covered by the backbone line identifier in the node set. The in-degree refers to the number of edges pointing to a node in a directed power supply topology. For a radial distribution network, the head-end node on the power supply side does not have any upstream power supply nodes supplying power to it, so its in-degree is zero. By traversing all nodes on the backbone line and checking their in-degree values ​​one by one, the unique node with an in-degree of zero is selected, which is the head-end node on the power supply side of the backbone line. The level depth of this node is marked as zero, the node type is marked as root node, and the parent node pointer is set to null, completing the initialization operation of the root node of the tree structure. The determination of the root node provides a unique starting anchor point for subsequent top-down hierarchical traversal.

[0019] Next, starting from the root node, a top-down breadth-first hierarchical traversal is performed on the node set based on the adjacency matrix constructed from the branch connection relationships. Parent-child adjacency relationships are identified layer by layer, and directed connections are established to generate an initial tree graph. Specifically, an adjacency matrix is ​​first constructed based on the branch connection relationship data in the distribution network feature parameter set. Assuming there are N nodes in the node set, an N x N matrix A is constructed. For any two nodes i and j in the node set, if there is a direct electrical connection line segment between them, the element values ​​in the i-th row and j-th column and the j-th row and i-th column of the adjacency matrix are both set to one; otherwise, they are set to zero. This results in a symmetric adjacency matrix that fully describes the direct connection relationships between all nodes in the network. Subsequently, the initialized root node is used as the starting node for the breadth-first traversal, and it is placed in a first-in-first-out traversal queue. Simultaneously, a set of visited node markers is created, and the root node is marked as visited. Specifically, the current node to be processed is retrieved from the head of the traversal queue. All non-zero elements in the corresponding row of the node in the adjacency matrix are queried to obtain all adjacent nodes with direct electrical connections to this node. For each adjacent node, it is checked whether it already exists in the visited node mark set. If the adjacent node has not yet been visited, it is marked as a child node of the currently processed node, a directed edge is established from the current processed node to the adjacent node, the level depth of the adjacent node is set to the level depth of the current processed node plus one, its parent node pointer is set to the current processed node, and then the adjacent node is added to the visited mark set and placed at the tail of the traversal queue for subsequent processing. If the adjacent node has already been visited, it is skipped to avoid duplicate edge construction. The above iterative process continues until the traversal queue is empty, meaning all reachable nodes have been visited and processed. For multi-branch nodes on the main line, all sub-branches extending to the right of the node are considered as a single multi-branch line and treated as child nodes of that node. After a complete breadth-first hierarchical traversal, all parent-child adjacency relationships and directed edges between nodes have been established, forming the initial tree diagram.

[0020] Then, loop closure detection and connectivity verification are performed on the initial tree diagram. After confirming that all nodes are free of loops and achieve complete coverage, the initial tree diagram is solidified and output as a distribution network tree structure diagram. Specifically, firstly, loop closure detection is performed to determine loops in the set of directed edges in the initial tree diagram. It verifies whether there is a closed path that starts from a node, goes through several intermediate nodes along the directed edge, and returns to the node itself. For a valid tree structure, there is one and only one unique path between any node and the root node, and there should be no loop structure. If a loop is detected, it indicates that there is an anomaly in the original topology data or a logical error in the traversal process, which needs to be backtracked, investigated, and corrected. Then, connectivity verification is performed by comparing the total number of nodes in the visited node mark set with the total number of nodes in the original node set. If the two are equal, it indicates that all nodes have been included in the tree diagram, achieving complete coverage, and there are no isolated nodes or unconnected subgraphs. If the two are not equal, it indicates that some nodes have not been traversed and the integrity of the original branch connection relationship data needs to be checked. Once the closed-loop detection confirms no loops and the connectivity check confirms complete coverage, all node information, level depth markers, parent-child adjacency relationships, and directed connection edge sets of the initial tree diagram are solidified and encapsulated, and the formal output is the distribution network tree structure diagram, which serves as the structured input for the subsequent step S2 fault observability constraint modeling.

[0021] Specifically, in step S2, based on the hierarchical adjacency relationship between parent and child nodes, fault observability constraint modeling is performed on each local node set in the distribution network tree structure diagram to obtain a set of fault observable linear constraints. It should be understood that the tree structure diagram itself only provides topological hierarchical information and has not yet established the mathematical constraints required for optimizing the placement of traveling wave location devices. Traveling wave location technology requires that when a fault occurs, there must be a device near the fault point capable of capturing traveling wave signals to achieve accurate fault location or section confirmation. In the tree topology of a radial distribution network, any line segment is connected between a parent node and one of its child nodes. If a fault occurs on this line, at least one node in the parent node or its child nodes must have a traveling wave location device installed to ensure that the fault traveling wave signal is effectively detected. Therefore, in the technical solution of this application, based on the hierarchical adjacency relationship between parent and child nodes in the tree structure diagram, a minimum coverage requirement for device configuration is established for each local area, forming mathematical constraints, thereby providing a feasible domain boundary for the subsequent step S3 to construct a zero-one integer programming model. The final set of linear constraints for fault observability is a set of linear inequalities formed by the simultaneous local algebraic constraints of all parent and child local node sets. Specifically, for each parent node and all its child nodes in the tree structure graph, at least one node has a traveling wave locator installed. This constraint set ensures that when a fault occurs on any line segment in the entire network, at least one traveling wave locator exists within the fault location area capable of capturing the fault's traveling wave signal, thus achieving direct or indirect fault observability. Direct fault observability means that traveling wave locators are installed on both sides of the fault point, allowing for precise fault location through the principle of double-ended ranging. Indirect fault observability means that a device is installed on only one side of the fault point, but the fault segment can be identified through device information from adjacent lines.

[0022] In practice, firstly, all non-leaf nodes in the distribution network tree structure diagram are traversed, and each parent node and all its directly connected child nodes are divided into an independent parent-child local node set. Specifically, a global scan of the distribution network tree structure diagram is performed first, checking the child node pointer set of each node one by one. If the child node pointer set of a node is not empty (i.e., the node has at least one directed connection edge pointing to the next level child node), then the node is marked as a non-leaf node and added to the list of parent nodes to be traversed; if the child node pointer set of a node is empty, then the node is a leaf node and is not added to the list of parent nodes. Subsequently, a local node set partitioning operation is performed on each non-leaf node in the parent node list: the numbers of all direct child nodes of the parent node are read, and the parent node itself and all its direct child nodes are encapsulated into an independent parent-child local node set. For a non-leaf node in a tree graph that is also a child node of another higher-level node, this node appears both as a child node in the local node set under its parent node and as the parent node itself has its own independent local node set. These two local node sets are independent of each other. After traversing all non-leaf nodes, multiple parent-child local node sets are obtained, equal in number to the number of non-leaf nodes. The union of these local node sets covers all nodes in the tree graph, and each line segment (i.e., each directed connection edge) is contained in at least one local node set.

[0023] Next, for each node entity in the parent-child local node set, a configuration state variable with a value of zero or one is assigned to obtain a local node set with state variables. Specifically, firstly, all candidate nodes in the distribution network tree structure diagram are arranged according to a unified index number. Assuming there are N candidate nodes in the entire network, a configuration state variable is assigned to the i-th candidate node. The value range of this variable is limited to two discrete integer values: zero and one, with the index i increasing from one to N. When the configuration state variable of the i-th node is one, it indicates that node i needs to install a traveling wave positioning device; when it is zero, it indicates that node i does not need to install the device. For each partitioned parent-child local node set, each node entity contained therein is replaced with the corresponding configuration state variable representation. Specifically, suppose a parent-child local node set consists of a parent node p and its set of direct child nodes, and this set of child nodes contains m child nodes, where m is the number of direct child nodes of the parent node p. Then, the configuration state variable set corresponding to this local node set contains the state variable of the parent node p and the state variables of all m of its child nodes, thus obtaining a local node set with state variables. Each local node set with state variables contains the configuration state variables of a parent node and the configuration state variables of all direct child nodes of that parent node. The total number of variables is the number of node entities in that local node set, i.e., m+1.

[0024] Furthermore, an algebraic constraint requiring the sum of state variables within a local region to be no less than one is applied to the local node set with state variables. This constraint is then combined with the algebraic constraints of all local regions to obtain a set of linear constraints for fault observability. Specifically, for each local node set with state variables, all configuration state variables are linearly summed, and the sum is required to be no less than one. Specifically, the configuration state variable of the parent node is added one by one to the configuration state variables of all its direct child nodes to obtain a linear summation expression. Then, a lower bound constraint greater than or equal to one is applied to this summation expression. Since each configuration state variable can only take the value of zero or one, when the state variables of all nodes in the local node set are zero, the summation result is zero, failing to meet the greater than or equal to one constraint requirement. This means that a scheme where no node in the local region has an installed device is infeasible. Conversely, as long as at least one node in the local node set has a state variable value of one, the summation result is greater than or equal to one, and the constraint is satisfied. This ensures that at least one traveling wave positioning device exists in the local region. In this way, within the local area formed by the parent node and all its direct child nodes, at least one node is equipped with a traveling wave positioning device, thereby ensuring that when a fault occurs in any line segment within the local area, the fault traveling wave signal can be captured by at least one device.

[0025] After applying the above constraint application operation to each non-leaf node in the distribution network tree structure diagram, multiple linear inequalities equal to the number of non-leaf nodes are obtained. Assuming there are K non-leaf nodes in the tree structure diagram, the combined local algebraic constraints form a fault observability linear constraint set containing K linear inequalities. These K inequalities constitute the fault observability linear constraint set, which covers the local regions corresponding to all parent-child adjacency relationships in the tree structure diagram, ensuring that any line segment in the entire network is within the observable range of at least one traveling wave location device. If a child node is itself a non-leaf node (i.e., it has a next-level child node), the same constraints are recursively applied to that child node and its child nodes, thereby ensuring that the constraints cover the complete tree hierarchy from the root node to all leaf nodes. The fault observability linear constraint set serves as the feasible region boundary of the zero-one integer programming model in subsequent step S3, limiting the value space of the decision variables, ensuring that the optimization solution process searches only within the feasible solution space that satisfies the fault observability of the entire network.

[0026] Specifically, in step S3, with the goal of minimizing the total number of installed devices, zero- and one-decision variables are assigned to all candidate nodes in the distribution network tree structure diagram, and the set of linear constraints for fault observability is embedded as the solution boundary to obtain the integer programming model for device placement. It should be understood that the set of linear constraints for fault observability across the entire network established in step S2 specifies the minimum configuration requirements for traveling wave location devices in each local area of ​​the distribution network tree structure diagram in the form of linear inequalities. However, the constraints themselves only define the feasible domain boundary of the device placement scheme, but do not provide an optimal judgment criterion. In engineering practice, the procurement, installation, and maintenance of traveling wave location devices require significant investment; the more devices there are, the higher the investment cost. Therefore, under the premise of ensuring the observability of faults across the entire network, the goal should be to minimize the total number of installed devices to achieve optimal economic efficiency. Therefore, in the technical solution of this application, the device placement problem is transformed into a mathematical programming model with a clear optimization objective and constraint boundary, enabling subsequent steps to use a professional solver to systematically search within the feasible solution space to find the globally optimal placement scheme with the theoretically minimum number of devices.

[0027] In practice, the process begins by extracting all physical nodes from the distribution network tree structure diagram and counting the total number of candidate nodes. Each candidate node is then assigned a zero- or one-decision variable and encapsulated into a network-wide decision variable vector according to its index sequence. Specifically, the distribution network tree structure diagram is first extracted by traversing the complete set of nodes from the root node to all leaf nodes. The node number of each physical node is read and added to the candidate node list. The number of nodes in the candidate node list is then counted to obtain the total number of candidate nodes, N. This value represents the total number of candidate locations in the entire distribution network where a traveling wave positioning device can be installed. After determining the total number of candidate nodes, N, each node in the candidate node list is assigned a zero- or one-decision variable according to its index number. The first candidate node is assigned the first decision variable, the second candidate node the second, and so on until the Nth candidate node is assigned the Nth decision variable. The value of each decision variable is strictly limited to two discrete integer values: zero and one. Finally, all N zero- and one-way decision variables are arranged in order from one to N according to their node indices, and encapsulated into a one-dimensional vector containing N elements, namely the network-wide decision variable vector X, where the i-th component of X corresponds to the zero- and one-way decision variable of the i-th candidate node. The construction of the network-wide decision variable vector completes the mapping from physical nodes to mathematical variables, providing a unified variable basis for the subsequent mathematical expression of objective functions and constraints.

[0028] Next, using the total number of candidate nodes as the accumulation boundary, a linear summation is performed on all elements of the network-wide decision variable vector, and a minimization operator is applied to construct a basic objective function equation oriented towards minimizing the total number of installed devices. Specifically, using the total number of candidate nodes N as the upper bound of the summation operation, a linear summation operation is performed on all components of the network-wide decision variable vector X from the first element to the Nth element. That is, the decision variables of the first candidate node, the second candidate node, the third candidate node, and so on are added sequentially up to the decision variable of the Nth candidate node, resulting in a linear summation expression for all decision variables. Specifically, since each decision variable only takes zero or one or two values, a variable with a value of one contributes one value to the summation (representing the installation of one device), and a variable with a value of zero contributes zero value to the summation (representing no device installation). Therefore, the linear summation result of all decision variables is numerically equal to the number of nodes in the network whose decision variables take a value of one, i.e., the total number of traveling wave positioning devices installed in the entire network. Subsequently, a minimization operator is applied to this linear summation expression. In other words, during the subsequent solution process, the solver will systematically search for various combinations of decision variable values ​​within the feasible solution space that satisfies all constraints, and find the combination of values ​​that minimizes the linear sum. This minimum value is the minimum number of devices required to ensure the observability of faults across the entire network. The construction of the basic objective function equation completes the mathematical definition of the optimization direction, clarifying that the solver's optimization objective is the global minimization of the total number of devices installed.

[0029] Furthermore, the fault-observable linear constraint set is used as the feasible region boundary and parameterized and formatted with the basic objective function equation to obtain the point-based integer programming model. Specifically, all K linear inequalities in the fault-observable linear constraint set are read one by one. The left side of each inequality is a linear summation expression of the decision variables corresponding to all nodes in a certain parent-child local node set, and the right side is a constant 1, with the inequality sign indicating greater than or equal to. These K linear inequalities are then parameterized with the decision variables in the basic objective function equation, confirming that each decision variable appearing in the constraints and the decision variables in the objective function belong to the same set of variables, sharing the same variable index and domain definition. The value of any decision variable in the objective function must be consistent with its value in the constraints. Subsequently, discrete value constraints for decision variables are added to the constraints. Specifically, it is explicitly stated that the domain of each element in the network-wide decision variable vector is a discrete set of integers, with indices i ranging from one to N. This constraint ensures that the installation decision for each node in the solution is a clear binary choice of "install" or "do not install," and does not allow continuous values ​​between zero and one. Finally, the minimization objective function, K fault observability linear inequality constraints, and N discrete value constraints for decision variables are compiled and assembled according to the format of a standard integer programming model, forming a complete point-based integer programming model. The overall structure of this model is as follows: the optimization objective part declares the minimum of the linear summation of all decision variables; the constraint part contains K linear inequalities guaranteeing the observability of faults across the entire network and N discrete value restrictions for decision variables (zero and one); these three parts together define a standard zero-one integer linear programming problem, possessing the structural characteristics of a linear objective function, linear constraints, and discrete decision variables, which can be directly recognized and processed by a mixed-integer linear programming solver. The construction of the point-based integer programming model completes the transformation from an engineering decision problem to a standard mathematical optimization problem, providing standardized model inputs for the weighted correction in step S4 and the exact solution in step S5.

[0030] Specifically, in step S4, based on line length data and historical fault frequency data, the comprehensive weight coefficient of each node is determined, and the objective function of the integer programming model for node placement is weighted and modified based on the comprehensive weight coefficient of each node to obtain a weighted integer programming model for node placement. It should be understood that in actual power distribution network engineering, the installation requirements for traveling wave location devices vary significantly among different nodes: long branch line terminus nodes far from the main line have a more urgent need for device configuration due to the long propagation path and severe attenuation of the traveling wave signal; line sections with high historical fault frequencies have a high probability of fault occurrence, and prioritizing device configuration near them can more effectively improve the actual fault location effect. If minimizing the total number of devices is the sole optimization guideline without considering the differentiated needs of each node, the solver may choose a scheme with the fewest devices but whose placement locations fail to prioritize coverage of critical lines when multiple equivalent optimal solutions exist, thus weakening the engineering practical value of the placement scheme. Therefore, in the technical solution of this application, the comprehensive weight coefficient of each node is calculated based on the line length data and historical fault frequency data, and embedded into the objective function to perform weighted correction on the coefficients of each decision variable. This enables the optimization solution process to automatically prioritize the allocation of limited device resources to the node positions corresponding to long lines and high failure rate lines while pursuing the minimization of the total number of devices, thereby achieving a high degree of adaptation between the deployment scheme and the actual operating conditions of the distribution network.

[0031] Figure 3 This is a flowchart of step S4 in the method for optimizing the placement of traveling wave positioning devices in a multi-branch complex distribution network according to an embodiment of this application. Figure 3 As shown, in the first embodiment of this application, step S4 includes: S41, normalizing the shortest path length from each candidate node to the midpoint of the trunk line in the line length data to obtain a line length weight array; S42, normalizing the fault frequency value of the line where each node is located in the historical fault frequency data, and then using a weight adjustment factor to linearly weight and fuse the line length weight array and the fault frequency normalization result to obtain a node comprehensive weight coefficient vector; S43, binding the node comprehensive weight coefficient vector to the coefficient position of the corresponding decision variable in the point-based integer programming model according to the index position to output the weighted point-based integer programming model.

[0032] Specifically, in step S41, the shortest path length from each candidate node to the midpoint of the main line in the line length data is normalized to obtain a line length weight array. Specifically, firstly, path length information for each candidate node is extracted from the line length data in the distribution network characteristic parameter set. For each candidate node i, the shortest path length from the end of the corresponding line to the midpoint of the main line is calculated. This length value is obtained by cumulatively adding the lengths of each line segment along the path back from the node to the midpoint of the main line in the tree structure diagram. Then, the average distance from all end nodes in the entire network to the midpoint of the main line is calculated. Finally, a line length normalization operation is performed on each candidate node i, that is, the shortest path length of the node is divided by the average distance constant to obtain the line length normalization weight value for that node. In other words, the path length of each node is standardized based on the average distance of the entire network. A normalization result greater than one indicates that the node's distance from the midpoint of the main line exceeds the average level, and the configuration requirement for the device is higher than average; a normalization result less than one indicates that the node's distance is lower than the average level, and the configuration requirement is relatively low. After performing the above normalization operation on all N candidate nodes one by one, the normalized weight values ​​of each node are arranged in order of node index and encapsulated as a line length weight array.

[0033] Specifically, in step S42, after normalizing the fault frequency values ​​of the lines where each node is located in the historical fault frequency data, a weight adjustment factor is used to linearly weight and fuse the line length weight array and the fault frequency normalization result to obtain the node comprehensive weight coefficient vector. Specifically, firstly, the historical fault frequency values ​​of the lines where each candidate node is located are extracted from the historical fault frequency data in the distribution network feature parameter set. For each candidate node i, the fault frequency value of the line segment where the node is located within the statistical period is read. Then, the maximum value is retrieved from the historical fault frequency data of all lines in the entire network, i.e., the fault frequency values ​​of all line segments are traversed and the maximum value is taken to obtain the maximum historical fault frequency extreme value of the entire network. Then, a fault frequency normalization operation is performed on each candidate node i. Specifically, the historical fault frequency of the line where the node is located is divided by the maximum historical fault frequency extreme value of the entire network to obtain the fault frequency normalized value of the node. In other words, the fault frequency of each node is standardized and measured based on the highest fault frequency in the entire network. The closer the normalization result is to one, the closer the fault frequency of the line where the node is located is to the highest level in the entire network, and the more urgent the need for the configuration of the device. The closer the normalization result is to zero, the lower the fault frequency of the line where the node is located, and the relatively weaker the need for configuration.

[0034] After normalizing the line length and fault frequency, a preset weight adjustment factor is introduced. For each candidate node i, the line length weight and fault frequency normalization result are linearly weighted and fused using the weight adjustment factor. Specifically, the weight adjustment factor is multiplied by the line length normalization weight value of the node to obtain the weighted contribution term of the line length attribute; then, the complementary value of the weight adjustment factor is multiplied by the fault frequency normalization value of the node to obtain the weighted contribution term of the fault frequency attribute; finally, the two weighted contribution terms are added to obtain the comprehensive weight coefficient of the node. In this process, the weight adjustment factor controls the contribution ratio of the line length attribute, and its complementary value controls the contribution ratio of the fault frequency attribute. The linear superposition of the two weighted results allows the comprehensive weight coefficient to simultaneously reflect the dual engineering requirements of the spatial distance dimension and the fault risk dimension. After performing the above fusion operation on all N candidate nodes one by one, the comprehensive weight coefficients of each node are arranged in order of node index and encapsulated as a node comprehensive weight coefficient vector.

[0035] Specifically, in step S43, the node comprehensive weight coefficient vector is bound one by one to the coefficient position of the corresponding decision variable in the integer programming model according to the index position to output the weighted integer programming model. Specifically, firstly, the basic objective function equation in the integer programming model is read. The structure of this equation is to find the minimum value after equal-weighted linear summation of all N decision variables, i.e., the coefficient before each decision variable is a unit of 1. Then, each element in the node comprehensive weight coefficient vector is bound one by one to the corresponding decision variable in the basic objective function according to the node index position. That is, the comprehensive weight coefficient of the first candidate node is bound to the coefficient position of the first decision variable, the comprehensive weight coefficient of the second candidate node is bound to the coefficient position of the second decision variable, and so on, until the comprehensive weight coefficient of the Nth candidate node is bound to the coefficient position of the Nth decision variable. In this way, the unit coefficient of 1 before each decision variable in the basic objective function is replaced with the comprehensive weight coefficient value of the corresponding node, so that the objective function changes from an equal-weighted summation form to a weighted summation form. After the replacement, each decision variable is multiplied by the comprehensive weight coefficient of its corresponding node, and then the sum is accumulated across the entire network. That is, the comprehensive weight coefficient of the first node is multiplied by the first decision variable, plus the comprehensive weight coefficient of the second node multiplied by the second decision variable, and so on, until the comprehensive weight coefficient of the Nth node is multiplied by the Nth decision variable. A minimization operator is then applied to this weighted sum. Since nodes with larger comprehensive weight coefficients have a higher contribution weight in the objective function, the solver, in order to minimize the weighted objective function value during the optimization process, will seek the solution with the minimum overall weighted sum while satisfying the observability constraints, thereby prioritizing the allocation of deployment resources towards long lines and lines with high failure rates. Finally, the weighted objective function is reassembled with the fault observability linear constraint group and the discrete value constraints of the decision variables in the original deployment integer programming model. The constraint conditions remain unchanged, and only the objective function part is weighted and corrected, thus outputting the weighted deployment integer programming model. The construction of the weighted integer programming model enhances the engineering adaptability of the basic model, providing an optimized model input that balances economic efficiency and engineering practicality for the accurate solution of the subsequent step S5.

[0036] Specifically, as described above, in the scenario of optimizing the deployment of traveling wave location devices in a radial distribution network, sub-step S42 of the first embodiment employs a simple normalization strategy based on individual fault frequencies to calculate the comprehensive weight of nodes—extracting the historical fault frequency values ​​of the lines where each candidate node is located, performing division normalization with the maximum historical fault frequency extreme value of the entire network as the denominator, and then linearly fusing it with the line length weight. This processing method treats each candidate node in the distribution network as an isolated independent individual, focusing only on the fault performance of the node's own lines, completely ignoring the inherent upstream and downstream path cascading fault coupling relationship in the radial tree topology.

[0037] However, radial distribution networks employ a single-source radial power supply structure, where electrical energy originates from the substation outlet (root node) and is transmitted layer by layer along the main lines and branch lines to the end load nodes. In this topology, the normal power supply to any end node depends entirely on the normal operation of all line segments along the complete ancestral path from the root node to that node. If any segment of the ancestral path experiences a short circuit or ground fault, that node and all its downstream child nodes will lose power, resulting in a cascading power outage effect. Taking an end node at the fourth level of a tree topology as an example, even if the historical fault frequency of the line it traverses is only 0.02 times / year, if the three lines along its ancestral path have fault frequencies of 0.15, 0.10, and 0.08 times / year respectively, the cumulative risk of power outage for that node is far higher than the level reflected by its own fault frequency. The first embodiment's weight assessment of such nodes systematically underestimates their importance, obtaining an extremely low weight ratio by dividing 0.02 by the maximum value of the entire network, failing to reflect the true vulnerability of the node in the overall network fault exposure pattern.

[0038] This approach of severing the inherent fault propagation coupling relationships between nodes in a tree topology directly results in the optimized deployment scheme failing to prioritize the deployment of traveling wave location devices on deep paths with high cumulative outage risk. When faults actually occur on the ancestral paths of these underestimated nodes, the lack of nearby traveling wave detection devices prolongs the fault location response time, expands the isolation range, and reduces power restoration efficiency, thus diminishing the engineering value of traveling wave location technology in intelligent operation and maintenance of distribution networks.

[0039] In view of the above-mentioned technical defects, this application further proposes a second embodiment.

[0040] Specifically, firstly, the constraint matrix encapsulated in the integer programming model is subjected to inverse topological analysis to reconstruct the ancestral path node sequence of each candidate node from the root node. Based on this sequence, the fault frequency values ​​of the lines where each ancestral node is located are queried from the historical fault frequency data, and arranged in hierarchical order to obtain a set of node ancestral path fault frequency sequences. Firstly, the complete ancestral power supply path of each candidate node is reconstructed, and the fault frequency data of each line segment along this path is extracted to form an ordered fault frequency propagation link.

[0041] Specifically, a reverse topology analysis is performed on the fault observable linear constraint matrix encapsulated in the integer programming model. By using the parent-child node coverage relationship in the constraint matrix to backtrack layer by layer, the complete ancestor path node sequence from the root node to itself in the tree structure is reconstructed for each candidate node. Then, using this ancestor path node sequence as the index key, the individual fault frequency value of the corresponding line in the historical fault frequency data is queried one by one. These values ​​are then arranged in an ordered manner according to the topological hierarchy from the root node to the current node, reconstructing a complete fault frequency propagation link from the power supply side to the load side for each candidate node. After performing the above operations on all candidate nodes in the entire network, the output is a set of node ancestor path fault frequency sequences.

[0042] After the above processing, the fault frequency data of each node, which was originally viewed in isolation, is re-embedded into the single-source power supply path structure of the radial distribution network. This enables the subsequent cumulative risk quantification calculation to perceive the cascading physical effect that upstream line faults will cause all downstream nodes to lose power, providing an orderly data foundation for accurately assessing the true status of each node in the overall fault exposure pattern of the network.

[0043] Next, the frequency sequences of each node in the ancestral path fault frequency sequence set are cumulatively calculated using path cascade to obtain the node cascade fault exposure array. That is, after obtaining the ancestral path fault frequency sequences of each node, these discrete line segment fault frequency values ​​are transformed into a unified scalar index that comprehensively reflects the actual power outage risk of that node. The power supply path of a radial distribution network essentially constitutes a series reliability system—a fault in any segment of the path will lead to power loss at the terminal node. Therefore, the principle of complementary reliability in series systems is used for cumulative probability calculation.

[0044] Specifically, for each candidate node's fault frequency sequence in the set of ancestral path fault frequency sequences, the fault frequency of each line segment in the sequence is first normalized to the maximum value across the entire network, mapping it to a probability dimension between 0 and 1. Then, the probability of no fault occurring for each line segment (i.e., 1 minus the normalized fault frequency of that segment) is multiplied together to obtain the joint probability of no fault along the entire path from the root node to that node. Finally, the joint probability of no fault along the entire path is subtracted from 1 to obtain the scalar of the path cascade fault exposure of that node. After performing the above calculations on all candidate nodes across the entire network, the results are encapsulated and output as a node cascade fault exposure array according to the node index.

[0045] The calculation process for path cascading fault exposure is as follows: in, Let be the path cascade fault exposure of the i-th candidate node, which represents the cumulative probability that the node will suffer a power outage due to a fault in any line on its ancestor path, and its value ranges from 0 to 1. The number of ancestor path segments of the i-th candidate node is the total number of path segments traversed from the root node to this node, which is determined by the level depth of this node in the tree topology. This is the path segment index used when traversing each segment of the ancestor path, with values ​​increasing from 1 to... ; The normalized fault frequency of the k-th segment of the ancestral path of the i-th candidate node is obtained by dividing the individual historical fault frequency of this segment by the maximum historical fault frequency extreme value of the entire network. This represents the probability that the k-th line segment will not experience a fault within the statistical period.

[0046] It should be noted that the longer the ancestral path and the higher the failure frequency of each segment along the route, the closer the product of the terms approaches zero, thus increasing the exposure. The closer the value is to 1, the more accurately it characterizes the high cumulative power outage risk of deep end nodes under the condition of multiple faulty lines connected in series for power supply. Compared with the first embodiment, which only divides the fault frequency of the node itself by the maximum value of the entire network, the path cascade fault exposure can truly reflect the actual vulnerability of deep end nodes in the tree topology, avoiding a systematic underestimation of the device configuration requirements of these high-risk nodes.

[0047] Furthermore, based on the weight adjustment factor, the line length weight array and the node cascade fault exposure array are fused and weighted to obtain the node comprehensive weight coefficient vector. That is, after obtaining the node cascade fault exposure array, it is fused with the line length weight array to generate a comprehensive weight coefficient that takes into account both spatial topological distance characteristics and path cascade fault exposure characteristics, so as to drive the subsequent integer programming model to achieve accurate deployment of site resources under limited device budget.

[0048] Specifically, a preset weight adjustment factor is introduced, and the elements in the line length weight array are multiplied and weighted. Simultaneously, the complementary value of this factor (1 minus the adjustment factor) is multiplied and weighted on the corresponding elements in the node cascade fault exposure array. The two weighting results for the same node are then linearly accumulated to obtain the fused comprehensive attribute score. The comprehensive attribute scores of all candidate nodes across the entire network are then aggregated and encapsulated into a node comprehensive weight coefficient vector by node index array.

[0049] Specifically, the calculation process for the comprehensive weighting coefficient is as follows: in, is the comprehensive weight coefficient of the i-th candidate node. The larger the value, the more urgent the need for the node to be equipped with the traveling wave positioning device. This is a preset weight adjustment factor, with a value range between 0 and 1, used to control the relative importance of line length attribute and cascade fault exposure attribute in the comprehensive evaluation; Let be the scalar of the shortest path length from the end of the line corresponding to the i-th candidate node to the midpoint of the main line; This is the average distance constant from all end nodes in the network to the midpoint of the backbone line; The normalized weight for the line length of the i-th node; The complementary value of the weighting adjustment factor is assigned to the weight ratio of the cascade fault exposure dimension; The path cascading fault exposure of the i-th candidate node is calculated from the previous step.

[0050] After the above fusion process, the comprehensive weighting coefficient can simultaneously reflect the engineering requirements in two dimensions: in terms of spatial distance, the ends of long lines far from the main trunk need to be prioritized for coverage to ensure the effective acquisition range of traveling wave signals; in terms of fault risk, nodes at the ends of paths with high cumulative power outage probability also need to be prioritized for device deployment to shorten fault location response time. The synergy between the two enables the optimized deployment scheme to accurately deploy positioning resources to the weakest links with the most severe fault exposure across the entire network, even with a limited number of devices.

[0051] Specifically, by introducing path-cascaded fault coupling relationships to improve the original weight calculation mechanism, the objective function of the optimized distribution model can be made aware of the inherent fault propagation coupling effect between upstream and downstream nodes in a radial distribution network without increasing additional hardware overhead. The improved comprehensive weight coefficient no longer evaluates each node as an isolated individual, but positions each node within the global fault exposure pattern of its complete power supply path. This allows the integer programming solver to automatically allocate limited traveling wave location device resources to the deep path ends with high cumulative outage risk during the optimization process.

[0052] At the engineering level, the second embodiment enables the deployment scheme to have stronger coverage targeting for weak areas in tree topologies with deeper levels and frequent ancestor path failures. When a fault occurs on these critical paths, the nearby traveling wave location devices can more quickly capture transient traveling wave signals and complete accurate ranging or segment confirmation, effectively shortening the fault location response time, reducing the fault isolation range, and improving power restoration efficiency. Meanwhile, since the second embodiment only introduces path cascading cumulative probability calculation in the weight calculation stage, without changing the constraint structure and solution framework of the integer programming model, it achieves a significant improvement in the engineering adaptability of the deployment scheme with extremely low computational cost while maintaining mathematical optimality.

[0053] Specifically, in step S5, a mixed-integer linear programming solver is used to precisely solve the weighted integer programming model to output the optimal placement scheme for each candidate node, including whether or not to install the traveling wave positioning device. It should be understood that step S4 has completed the construction of the weighted integer programming model, which includes a weighted objective function, a set of linear constraints for fault observability, and zero-to-one discrete value constraints for decision variables, fully defining the mathematical expression of the traveling wave positioning device optimization placement problem. However, the mathematical model itself is only a formal description of the optimization problem and does not yet provide a specific optimal solution; that is, it has not yet determined whether the decision variable for each candidate node should be zero or one. Zero-to-one integer programming is a combinatorial optimization problem, and the size of its feasible solution space grows exponentially with the number of candidate nodes. For a problem with N candidate nodes, theoretically there are 2^N possible combinations of decision variable values. However, exhaustively evaluating the feasibility and objective function value of each combination is unacceptable in engineering practice. Therefore, the technical solution of this application employs a professional mixed-integer linear programming solver. Utilizing its built-in branch-and-bound algorithm and other precise solution techniques, it performs a systematic intelligent search within the feasible solution space to efficiently find the optimal combination of decision variable values ​​that minimizes the weighted objective function, thereby outputting a placement scheme with mathematical optimality guarantees. The mixed-integer linear programming solver ensures that the obtained solution is globally optimal rather than locally optimal, guaranteeing that the placement scheme theoretically minimizes the number of devices while satisfying the overall network fault observability requirement.

[0054] In practice, the first step is to initialize the runtime environment of the mixed-integer linear programming solver. This involves injecting the weighted objective function, observable constraint matrix, and discrete variable attributes from the weighted integer programming model into the solver according to the standard interface specifications to obtain a solver-ready instance. Specifically, the first step is to select the specific implementation software for the mixed-integer linear programming solver, such as Gurobi, CPLEX, SCIP, or equivalent optimization software. A runtime instance of the solver is created, and environment preparation work such as memory allocation and parameter initialization is completed. Then, each component of the weighted integer programming model is injected one by one according to the standard interface specifications required by the solver. Specifically, the definition information of the decision variables is injected first: declaring that there are N decision variables in the entire network, each decision variable being a binary integer variable (i.e., a zero-one variable), with a value range of zero and one, and variable indices numbered sequentially from one to N. Then, the information of the weighted objective function is injected: the N elements in the node comprehensive weight coefficient vector are used as the linear coefficients of each decision variable in the objective function, and are passed to the solver in index order. Simultaneously, the optimization direction is declared as minimization, meaning the solver needs to find the combination of variable values ​​that minimizes the sum of the products of each decision variable and its corresponding weight coefficient. Next, the information of the fault observable constraint matrix is ​​injected: the K linear inequality constraints established in step S2 are converted into matrix form, where each row of the constraint matrix corresponds to an inequality, and the elements in each column of the row are the coefficients of the corresponding decision variables in that inequality (the coefficients of nodes appearing in the parent-child local node set are one, and the coefficients of nodes not appearing are zero), each element of the right-hand constant vector is one, and the inequality direction is always greater than or equal to. The constraint matrix, the right-hand constant vector, and the inequality direction information are passed to the solver according to the standard interface format. After all information is injected, the solver performs format verification and consistency checks on the input data to confirm that the objective function coefficient dimension is consistent with the number of variables, the number of columns in the constraint matrix is ​​consistent with the number of variables, and all numerical parameters are within a reasonable range. After the verification is passed, the solver enters the ready state and a solver ready instance is obtained.

[0055] Next, the branch-and-bound optimization engine of the solver-ready instance is triggered. Under the premise of satisfying all constraints, a global search iteration is performed within the zero-one discrete feasible solution space. After convergence, the deterministic values ​​of each decision variable that achieve the global minimum of the weighted objective function are extracted, and the optimal Boolean vector set is output. Specifically, first, a solution start command is sent to the solver-ready instance, triggering its built-in branch-and-bound optimization engine to begin computation. Specifically, linear relaxation is first performed on the original zero-one integer programming problem, that is, the zero-one discrete value constraints of each decision variable are temporarily relaxed to continuous values ​​between zero and one, transforming the problem into a standard continuous linear programming problem and solving it. The optimal solution of the relaxed problem and the corresponding objective function value are used as a lower bound estimate of the global optimum of the original problem. If the optimal solution of the relaxed problem exactly satisfies that all variables take integer values ​​of zero or one, then this solution is the global optimum of the original problem, and the solution process ends directly. If the optimal solution to the relaxation problem contains non-integer variables with values ​​between zero and one, then one of these non-integer variables is selected for branching, decomposing the current problem into two subproblems: one subproblem forces the variable to a value of zero, and the other subproblem forces the variable to a value of one. The relaxation linear programming problem for each subproblem is solved separately, obtaining a lower bound estimate for each subproblem. During the search process, whenever a relaxation solution to a subproblem satisfies all integer constraints, a feasible integer solution is obtained. Its objective function value is compared with the currently known optimal upper bound. If it is better than the current optimal upper bound, the optimal upper bound and the corresponding optimal feasible solution are updated. Whenever the relaxation lower bound of a subproblem is greater than or equal to the current optimal upper bound, it indicates that no feasible integer solution to that subproblem can be better than the known optimal solution, and the subproblem can be pruned and discarded without further exploration. The branch-and-bound optimization engine iterates repeatedly according to the above branching, bounding, and pruning logic, gradually narrowing the search space and converging the gap between the upper and lower bounds until all unpruned subproblems have been solved. At this point, the upper and lower bounds converge to the same value, and the algorithm terminates. The optimal feasible integer solution retained upon convergence is the global optimal solution of the weighted integer programming model in the zero-one discrete feasible solution space. It possesses a mathematically provable optimality guarantee, meaning that no other combination of zero-one values ​​satisfying all constraints can result in a smaller value for the weighted objective function. The deterministic values ​​of each decision variable are extracted from the converged solution results. The final values ​​of the N decision variables are arranged in index order and encapsulated, ultimately outputting the optimal Boolean vector set.

[0056] Then, the elements with a state value of one in the optimal Boolean vector set are reverse-mapped back to the actual physical nodes of the distribution network according to their indices to obtain the optimal deployment scheme. Specifically, first, all N elements in the optimal Boolean vector set are read, and the value state of each element is checked one by one. For elements with a value of one, the correspondence table between node indices and physical node numbers established in step S3 is looked up according to their index position in the vector. The index position is reverse-mapped back to the corresponding actual physical node number in the distribution network tree structure diagram to confirm that the physical node is the target node that needs to install the traveling wave positioning device, and it is added to the installation node list. For elements with a value of zero, it is confirmed that the corresponding physical node does not need to install the device and is not included in the installation node list. After traversing all N elements to complete the reverse mapping, the installation node list contains all the physical node numbers that need to install the traveling wave positioning device. The number of nodes in the list is the minimum total number of devices required for the entire network. The installation node list and the total number of devices are formatted and sorted, and the output is the optimal deployment scheme. This optimal deployment scheme clearly indicates the specific node locations where traveling wave location devices need to be installed in the distribution network, as well as the minimum total number of devices required to ensure the observability of faults across the entire network. It can directly guide the engineering deployment and implementation of traveling wave location devices in the distribution network.

[0057] In summary, the optimized deployment method for traveling wave location devices in multi-branch complex distribution networks according to the embodiments of this application is explained. It transforms the topology of the radial distribution network into a tree-like hierarchical model, establishes a linear constraint system for observable faults across the entire network based on the adjacency relationship between parent and child nodes, constructs a zero-one integer programming model with the objective of minimizing the total number of devices installed, and introduces a weighted correction of the objective function using a combination of line length and historical fault frequency. Finally, an accurate solution is achieved through a mixed-integer linear programming solver. This approach significantly reduces the number of traveling wave location devices deployed, substantially lowers equipment investment costs, ensures the global optimality and reproducibility of the optimization results, and the weighting mechanism makes the deployment scheme highly adaptable to the actual operating conditions of the distribution network, effectively improving the engineering practical value of fault location.

[0058] Furthermore, an optimized deployment system for traveling wave positioning devices in complex multi-branch power distribution networks is also provided.

[0059] Figure 4 A block diagram illustrating the optimized deployment system for traveling wave location devices in a multi-branch complex distribution network according to embodiments of this application. Figure 4As shown, the traveling wave location device optimization deployment system 300 for a multi-branch complex distribution network according to an embodiment of this application includes: a tree recursive transformation module 310, used to perform tree recursive transformation on the acquired distribution network feature parameter set based on the hierarchical topology of the radial distribution network to obtain a distribution network tree structure diagram; a fault observability constraint modeling module 320, used to perform fault observability constraint modeling on each local node set in the distribution network tree structure diagram based on the hierarchical adjacency relationship between parent and child nodes to obtain a fault observability linear constraint set; and an integer programming modeling module 330 with a minimization objective, used to optimize the distribution network tree structure with the minimization of the total number of installed devices as the optimization objective. All candidate nodes in the diagram are assigned zero- or one-decision variables, and the fault observable linear constraint set is embedded as the solution boundary to obtain the point placement integer programming model. The refined modeling module 340 with comprehensive weight correction is used to determine the comprehensive weight coefficient of each node based on the line length data and historical fault frequency data, and to perform weighted correction on the objective function of the point placement integer programming model based on the comprehensive weight coefficient of each node to obtain the weighted point placement integer programming model. The mixed integer programming accurate solution module 350 is used to use a mixed integer linear programming solver to accurately solve the weighted point placement integer programming model to output the optimal point placement scheme for whether to install traveling wave positioning devices on each candidate node.

[0060] As described above, the traveling wave positioning device optimization deployment system 300 for multi-branch complex distribution networks according to embodiments of this application can be implemented in various wireless terminals, such as servers with traveling wave positioning device optimization deployment algorithms for multi-branch complex distribution networks. In one possible implementation, the traveling wave positioning device optimization deployment system 300 for multi-branch complex distribution networks according to embodiments of this application can be integrated into a wireless terminal as a software module and / or a hardware module. For example, the traveling wave positioning device optimization deployment system 300 for multi-branch complex distribution networks can be a software module in the operating system of the wireless terminal, or it can be an application developed for the wireless terminal; of course, the traveling wave positioning device optimization deployment system 300 for multi-branch complex distribution networks can also be one of many hardware modules of the wireless terminal.

[0061] Alternatively, in another example, the traveling wave positioning device optimization deployment system 300 for the multi-branch complex power distribution network and the wireless terminal can also be separate devices, and the traveling wave positioning device optimization deployment system 300 for the multi-branch complex power distribution network can be connected to the wireless terminal via wired and / or wireless networks, and transmit interactive information in accordance with the agreed data format.

[0062] The various embodiments of this disclosure have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is chosen to best explain the principles, practical application, or improvement of the technology in the market, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A method for optimizing the placement of traveling wave positioning devices in a complex multi-branch power distribution network, characterized in that, include: S1. Based on the hierarchical topology of the radial distribution network, the obtained distribution network feature parameter set is recursively transformed into a tree structure to obtain the distribution network tree structure diagram. S2, based on the hierarchical adjacency relationship between parent and child nodes, performs fault observability constraint modeling on each local node set in the distribution network tree structure diagram to obtain a fault observability linear constraint set; S3, with the optimization objective of minimizing the total number of installed devices, assigns zero-one decision variables to all candidate nodes in the distribution network tree structure diagram, and embeds the fault observable linear constraint set as the solution boundary to obtain the point layout integer programming model; S4. Based on the line length data and historical fault frequency data, determine the comprehensive weight coefficient of each node, and perform weighted correction on the objective function of the integer programming model based on the comprehensive weight coefficient of each node to obtain the weighted integer programming model. S5 employs a mixed-integer linear programming solver to accurately solve the weighted point-based integer programming model, thereby outputting the optimal point-based scheme for whether or not to install traveling wave positioning devices at each candidate node.

2. The optimized placement method for traveling wave positioning devices in multi-branch complex distribution networks according to claim 1, characterized in that, The distribution network characteristic parameter set includes node set, branch connection relationship, trunk line identification, line length data and historical fault frequency data.

3. The optimized placement method for traveling wave positioning devices in multi-branch complex distribution networks according to claim 2, characterized in that, Step S1 includes: Based on the backbone line identifier, the first end location retrieval is performed in the node set, the power supply side endpoint with zero in-degree in the backbone line is extracted, and it is initialized as the root node of the tree structure. Starting from the root node, based on the adjacency matrix constructed according to the branch connection relationship, a top-down breadth-first hierarchical traversal is performed on the node set to identify the parent-child adjacency relationship and establish directed connection edges layer by layer, generating an initial tree graph. Perform closed-loop detection and connectivity verification on the initial tree diagram. After confirming that there are no loops in all nodes and that full coverage is achieved, the initial tree diagram is fixed and output as a distribution network tree structure diagram.

4. The optimized placement method for traveling wave positioning devices in multi-branch complex distribution networks according to claim 1, characterized in that, Step S2 includes: Traverse all non-leaf nodes in the tree structure diagram of the power distribution network, and divide each parent node and all its directly connected child nodes into an independent set of parent and child local nodes; For each node entity in the parent-child local node set, assign a configuration state variable with a value of zero or one to obtain a local node set with state variables; Apply an algebraic constraint that the sum of the state variables within the local region is not less than one to the local node set with state variables, and then solve the algebraic constraints of all local regions to obtain the fault observable linear constraint set.

5. The optimized placement method for traveling wave positioning devices in multi-branch complex distribution networks according to claim 1, characterized in that, Step S3 includes: Extract all physical nodes from the distribution network tree structure diagram and count the total number of candidate nodes. Assign zero-one decision variables to each candidate node and encapsulate them into a network-wide decision variable vector according to the index sequence. Using the total number of candidate nodes as the cumulative boundary, linear summation is performed on all elements in the decision variable vector of the entire network and a minimization operator is applied to construct a basic objective function equation oriented towards minimizing the total number of installed devices. The fault-observable linear constraint set is used as the feasible region boundary and the basic objective function equation for parameter binding and formatted compilation to obtain the point-based integer programming model.

6. The optimized placement method for traveling wave positioning devices in multi-branch complex distribution networks according to claim 1, characterized in that, Step S4 includes: The shortest path length from each candidate node to the midpoint of the main line in the line length data is normalized to obtain the line length weight array. After normalizing the fault frequency values ​​of the lines where each node is located in the historical fault frequency data, the line length weight array and the fault frequency normalization result are linearly weighted and fused using a weight adjustment factor to obtain the node comprehensive weight coefficient vector. The node comprehensive weight coefficient vector is bound one by one to the coefficient position of the corresponding decision variable in the point-based integer programming model according to the index position to output the weighted point-based integer programming model.

7. The optimized placement method for traveling wave positioning devices in multi-branch complex distribution networks according to claim 1, characterized in that, Step S5 includes: Initialize the runtime environment of the mixed integer linear programming solver, and inject the weighted objective function, observable constraint matrix and discrete variable properties from the weighted point integer programming model into the solver according to the standard interface specification to obtain a solver ready instance; Trigger the branch-bound optimization engine of the solver-ready instance, and perform a global search iteration in the zero-one discrete feasible solution space under the premise of satisfying all constraints. After convergence, extract the deterministic values ​​of each decision variable that make the weighted objective function achieve the global minimum, and output the optimal Boolean vector set. The elements with a state value of one in the optimal Boolean vector set are reverse-mapped back to the actual physical nodes of the distribution network according to their index to obtain the optimal node layout scheme.

8. The optimized placement method for traveling wave positioning devices in multi-branch complex distribution networks according to claim 6, characterized in that, After normalizing the fault frequency values ​​of the lines where each node is located in the historical fault frequency data, a linear weighted fusion of the line length weight array and the fault frequency normalization result is performed using a weight adjustment factor to obtain the node comprehensive weight coefficient vector, including: Inverse topological analysis is performed on the constraint matrix encapsulated in the point-based integer programming model to restore the ancestor path node sequence of each candidate node from the root node to itself. Based on this sequence, the fault frequency value of the line where each ancestor node is located in the historical fault frequency data is queried and arranged in hierarchical order to obtain the set of node ancestor path fault frequency sequences. The path concatenation cumulative calculation is performed on the frequency sequence of each node in the node ancestor path failure frequency sequence set to obtain the node concatenation failure exposure array. Based on the weight adjustment factor, the line length weight array and the node cascade fault exposure array are fused and weighted to obtain the node comprehensive weight coefficient vector.

9. An optimized deployment system for traveling wave positioning devices in a complex multi-branch power distribution network, characterized in that, include: The tree recursive transformation module is used to perform tree recursive transformation on the obtained distribution network feature parameter set based on the hierarchical topology of the radial distribution network to obtain the distribution network tree structure diagram. The fault observability constraint modeling module is used to perform fault observability constraint modeling on each local node set in the distribution network tree structure diagram based on the hierarchical adjacency relationship between parent and child nodes to obtain a fault observability linear constraint set. The minimization objective integer programming modeling module is used to minimize the total number of installed devices as the optimization objective. It assigns zero-one decision variables to all candidate nodes in the distribution network tree structure diagram and embeds the fault observable linear constraint set as the solution boundary to obtain the point layout integer programming model. The refined modeling module with comprehensive weight correction is used to determine the comprehensive weight coefficient of each node based on line length data and historical fault frequency data, and to perform weight correction on the objective function of the integer programming model based on the comprehensive weight coefficient of each node to obtain the weighted integer programming model. The mixed-integer programming exact solution module is used to use a mixed-integer linear programming solver to accurately solve a weighted point-based integer programming model and output the optimal point-based scheme for whether to install traveling wave positioning devices on each candidate node.

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